Brodie Clarke, the suspended head of the UK Border Agency, has quit his job after being blamed by Theresa May for the relaxation of border checks which let an unknown number of illegal immigrants in to Britain.

In an explosive statement issued this evening he said he was being scapegoated unfairly for the "political convenience" of the home secretary and intended to sue for constructive dismissal.

He said: "I am anxious to take part in any independent inquiry into matters relating to UK Border Agency but my position at UKBA had been made untenable because of the statements made in the House of Commons by the Home Secretary Theresa May.

"Those statements are wrong and were made without the benefit of hearing my response to formal allegations. With the home secretary announcing and repeating her view that I am at fault, I cannot see how any process conducted by the Home Office or under its auspices, can be fair and balanced."

Clarke has been summoned to appear before the Commons home affairs committee next week. Now he has resigned from the civil service he will be freer to express his mind to MPs.

Had he still been in post he could technically even have been blocked from attending the session by May.

Clarke added: "The home secretary suggests that I added additional measures, improperly, to the trial of our risk-based controls. I did not. Those measures have been in place since 2008/09."

"I deeply regret having to make this statement. I am saddened that my career should end in such a way after 40 years of dedicated service. My employer has disregarded my right to reply in favour of political convenience."

The home secretary has said there is "no question" of her resigning over the fiasco. But Clarke's statement and potential comments to the committee do place her position under threat, especially if she is shown to have misled Parliament.

In a grilling by MPs on the home affairs committee on Tuesday morning, May heaped blame on UKBA officials, particularly Clark.

She reiterated her claim from Monday that a limited pilot had been taking place at points of entry to the country, involving reduced checks for some types of passengers, but she insisted that officials had gone too far in routinely relaxing passport checks.

Tellingly, Theresa May was extremely coy over whether she'd always had confidence in Clark. "He was the head of the UK Border Force," she simply said. But she added that she didn't suspend Clark directly. That had been done by Home Office officials.

May told MPs that Clark had asked her for permission to expand the relaxations under the pilot further, but she had rejected his proposals. However she seemed hazy on the details of how widespread the changes under the pilot that she sanctioned had been used.

"The pilot was made available for operation at all ports. It was not used at all ports," she said. But she was unable to answer exactly at which ports and airports the measures under the pilot were used.

She was also unable to answer how many times the level of checking of passports was reduced under the pilot scheme, but agreed to provide the answer to this by Friday.

In an echo of a previous home secretary's claim that the UKBA was "not fit for purpose", May told MPs: "We've all known for many years that UKBA has systemic problems and a culture that lacks a sense of responsibility."

May is also due to appear in the Commons tomorrow as Laboru have scheduled a debate on the border agency in an attempt to ramp up the pressure on the home secretary.

Yvette Cooper MP, Labour's shadow home secretary, responding to the resignation of Brodie Clark, said May had lost control of the British border.

"This fiasco gets worse for the home secretary. Now her version of events has been contradicted by her most senior official at the UK Border Force. First she decided to reduce border checks then lost control of her so called 'pilot,'" she said.

"Now she has lost the loyalty of one of her most senior civil servants. The home secretary clearly doesn't know what has been happening at our borders.

"She needs to come to Parliament tomorrow and answer these points urgently. And this shows it is even more important she publishes all the guidance and instructions she gave the border agency so we can tell what has really been going on."